Combinatorics Topics For K-8 TeachersMAT 305 Summer 1997

Roger Dayday@ilstu.edu

1.

A mathematics educator is planning to survey various
professionals. Surveys will be sent to 44 biologists, 29
chemists, 37 physicists, 51 endocrinologists, and 22
epidemiologists. How many responses must the mathematics
educator receive in order to guarantee that there will be at
least 20 responses from the same professional group?

Two rooks on a chessboard attack each other if they are
on the same row or the same column. Determine the number of
ways in which 8 non-attacking identical rooks can be placed
on the chessboard shown here. Squares with an "X" indicate
forbidden positions that cannot be occupied.